157
Views
159
CrossRef citations to date
0
Altmetric
Theory and Methods

The Maximal Smoothing Principle in Density Estimation

Pages 470-477 | Received 01 Oct 1988, Published online: 28 Feb 2012

References

  • Bemesderfer , K. and May , J. D. 1972 . Social and Political Inquiries , Belmont , CA : Duxbury Press .
  • Bowman , A. W. 1984 . An Alternative Method of Cross-Validation for the Smoothing of Density Estimates . Biometrika , 65 : 521 – 528 .
  • Deheuvels , P. 1977 . Estimation Nonparametrique de la Densite par Histogrammes Generalises II . Publications de l'Institute Statistiques de l'Universite Paris , 22 : 1 – 23 .
  • Devroye , L. and Gyorfi , L. 1985 . Density Estimation: The L1 View , New York : John Wiley .
  • Donoho , D. L. 1988 . One-Side Inference About Functionals of a Density I . The Annals of Statistics , 16 : 1390 – 1420 .
  • Epanechnikov , V. A. 1969 . Nonparametric Estimators of a Multivariate Probability Density . Theory of Probability and Its Applications , 14 : 153 – 158 .
  • Freedman , D. , Pisani , R. and Purves , R. 1979 . Statistics , New York : W. W. Norton .
  • Gasser , T. , Müller , H. G. and Mammitzsch , V. 1985 . Kernels for Nonparametric Curve Estimation . Journal of the Royal Statistical Society , 47 : 238 – 252 . Ser. B
  • Good , I. J. and Gaskins , R. A. 1980 . Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data . Journal of the American Statistical Association , 75 : 42 – 56 .
  • Hall , P. and Marron , J. S. 1987 . On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator . The Annals of Statistics , 15 : 163 – 181 .
  • Jaynes , E. T. 1957 . Information Theory and Statistical Mechanics . Physical Review , 106 : 620 – 630 .
  • Parzen , E. 1962 . On the Estimation of Probability Density Function and Mode . The Annals of Mathematical Statistics , 33 : 1065 – 1076 .
  • Rice , J. 1984 . Boundary Modification for Kernel Regression . Communications in Statistics, Part A , 13 : 893 – 900 .
  • Rudemo , M. 1982 . Empirical Choice of Histogram and Kernel Density Estimators . Scandinavian Journal of Statistics , 9 : 65 – 78 .
  • Schuster , E. F. 1985 . Incorporating Support Constraints Into Nonparametric Estimators of Densities . Communications in Statistics–Theory and Methods , 14 : 1123 – 1136 .
  • Scott , D. W. 1979 . On Optimal and Databased Histograms . Biometrika , 66 : 605 – 610 .
  • Scott , D. W. 1985 . Frequency Polygons: Theory and Applications . Journal of the American Statistical Association , 80 : 348 – 354 .
  • Scott , D. W. , Gotto , A. M. , Cole , J. S. and Gorry , G. A. 1978 . Plasma Lipids as Collateral Risk Factors in Coronary Artery Disease . Journal of Chronic Diseases , 31 : 337 – 345 .
  • Scott , D. W. and Terrell , G. R. 1987 . Biased and Unbiased Cross-Validation in Density Estimation . Journal of the American Statistical Association , 82 : 1131 – 1146 .
  • Silverman , B. W. 1983 . “ Some Properties of a Test for Multimodality Based on Kernel Density Estimates ” . In Probability, Statistics, and Analysis , Edited by: Kingman , J. E. C. and Reuter , G. E. H. 248 – 259 . Cambridge , , UK : Cambridge University Press .
  • Silverman , B. W. 1986 . Density Estimation in Statistics and Data Analysis , London : Chapman & Hall .
  • Terrell , G. R. 1985 . Projection Pursuit Via Multivariate Histograms , Rice University, Dept. of Mathematical Sciences . Technical Report 85–7
  • Terrell , G. R. and Scott , D. W. 1985 . Oversmoothed Nonparametric Density Estimates . Journal of the American Statistical Association , 80 : 209 – 214 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.